Big O Notation practice

Step One: Simplifying Expressions

1. O(n + 10) --> O(n)
2. O(100 * n) --> O(n)
3. O(25) --> O(1)
4. O(n^2 + n^3) --> O(n^3)
5. O(n + n + n + n) --> O(n)
6. O(1000 * log(n) + n) --> O(n)
7. O(1000 * n * log(n) + n) --> O(n log n)
8. O(2^n + n^2) --> O(2^n)
9. O(5 + 3 + 1) --> O(1)
10. O(n + n^(1/2) + n^2 + n * log(n)^10) --> O(n^2)

Step 2: Calculating Time Complexity

• function logUpto(n) --> O(n)
• function logAtLeast10(n) --> O(n)
• function logAtMost10(n) --> O(1)
• function onlyElementsAtEvenIndex(array) --> O(n)
• function sbutotals(array) --> O(n^2)
• function vowelCount(str) --> O(n)

Part 3 - short answer

1. True
2. True
3. False
4. O(n)
5. O(n)
6. O(n)
7. O(n log n)
8. O(n)
9. O(n)
10. O(1)
11. O(n)
12. O(n)